Question

Find the sum of first n natural numbers.

Answer 1

We know first $n$ natural numbers are

$1,2,\mathrm{3.......}n$

let $S=1+2+3+......+n$

write in reverse order we get

$S=n+n-1+n-2+.....+1$

$2S=\underset{ntimes}{\underset{}{(n+1)+(n+1)+........+(n+1)}}$

$2S=n(n+1)$

$S=\frac{n(n+1)}{2}$.